List questions from elementary-number-theory

64

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How to simplify this equality: $\sum_{i=1}^{n}\sum_{d\mid i} (\lfloor \frac{i}{d+1} \rfloor + \lfloor \frac{i}{d-1} \rfloor)$?

Published on 15 Apr 2026 - 23:11

88

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Ambiguity in abbreviation $a<b$

Published on 11 Apr 2026 - 21:32

453

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Dirichlet L-function and convergence of $\sum\limits_p \frac{\chi(p)}{p}$

Published on 13 Apr 2026 - 2:59

236

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Parity of sum of powers of odd numbers

Published on 14 Apr 2026 - 9:09

674

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Is it true that $n!$ divides $p^n(p+1)(p^2+p+1)\cdots(p^{n-1}+\cdots+1)$?

Published on 16 Apr 2026 - 19:39

107

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Primes of the form $p_1p_2\dotsm p_k+1$

Published on 14 Apr 2026 - 21:35

39

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What is known about the equation $p^i + q^j = 2^k$?

Published on 11 Apr 2026 - 15:09

62

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RSA repeated exponentiation

Published on 10 Apr 2026 - 21:41

122

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Numeralwise expressibility in logic

Published on 12 Apr 2026 - 13:56

77

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Primes congruent to $k \pmod p$ between $p$ and $p^2$?

Published on 14 Apr 2026 - 11:48

219

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The term “remainder” and IMO 2005, problem 2

Published on 14 Apr 2026 - 17:34

100

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Generating prime factors of a certain congruence?

Published on 29 Apr 2026 - 12:49

119

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Prove that any polynomial with integer coefficients must have a composite number in its image.

Published on 14 Apr 2026 - 1:23

96

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Did I find a mistake in a classic proof? If not, could someone help me understand?

Published on 09 Apr 2026 - 7:31

261

Views

Generating Pythagorean triples

Published on 11 Apr 2026 - 16:27

List Question

How to simplify this equality: $\sum_{i=1}^{n}\sum_{d\mid i} (\lfloor \frac{i}{d+1} \rfloor + \lfloor \frac{i}{d-1} \rfloor)$?

Ambiguity in abbreviation $a<b$

Dirichlet L-function and convergence of $\sum\limits_p \frac{\chi(p)}{p}$

Parity of sum of powers of odd numbers

Is it true that $n!$ divides $p^n(p+1)(p^2+p+1)\cdots(p^{n-1}+\cdots+1)$?

Primes of the form $p_1p_2\dotsm p_k+1$

What is known about the equation $p^i + q^j = 2^k$?

RSA repeated exponentiation

Numeralwise expressibility in logic

Primes congruent to $k \pmod p$ between $p$ and $p^2$?

The term “remainder” and IMO 2005, problem 2

Generating prime factors of a certain congruence?

Prove that any polynomial with integer coefficients must have a composite number in its image.

Did I find a mistake in a classic proof? If not, could someone help me understand?

Generating Pythagorean triples

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